What is area 2x+y^2=48,x=y ?

The answer to area 2x+y^2=48,x=y is 686/3

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area 2x+y^2=48,x=y

area

2 x + y^{2} = 48, x = y

\frac{686}{3}

Decimal Notation

228.66666 \dots

Solution steps

Isolate

y

for

2 x + y^{2} = 48 : y = 48 - 2 x, y = - 48 - 2 x

Isolate

y

for

x = y : y = x

f_{1} (x) = 48 - 2 x

f_{2} (x) = - 48 - 2 x

To find the intersection points solve

f_{i} (x) = f_{j} (x)

48 - 2 x = - 48 - 2 x : x = 24

48 - 2 x = x : x = 6

- 48 - 2 x = x : x = - 8

= \int_{- 8}^{6} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{6}^{24} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 8}^{6} - 48 - 2 x - x d x + \int_{6}^{24} 48 - 2 x - (- 48 - 2 x) d x

\int_{- 8}^{6} - 48 - 2 x - x d x = \frac{254}{3}

\int_{6}^{24} 48 - 2 x - (- 48 - 2 x) d x = 144

= \frac{254}{3} + 144

Simplify

= \frac{686}{3}

y^{^{'}} + 3 y = 4 sin (e^{3 x})

\int \frac{13}{25 - 9 x ^{2}} d x

\frac{( 2 x ^{2} + 3 x )}{4 x ^{2}}

\frac{d}{d x} (a x sin (2 x) + b x cos (2 x))

\frac{d x}{d t} = - \frac{50}{π} x^{- \frac{3}{2}}